How do you evaluate the sum represented by sum_(n=1)^(8)1/(n+1)8n=11n+1 ?

1 Answer
Oct 22, 2014

Begin by changing the denominators to 1+1, 2+1, 3+11+1,2+1,3+1 and so on to 8+1...

Next add 1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9

This requires a common denominator. If we multiply 9*8*7*5 we will get 2520.

The 9 picks up multiples of the 3, the and the 8 picks up multiples of the 2, 3 and 4.

Now, multiply 1/2*1260/1260 giving 1260/2520. Multiply 1/3*840/840 giving 840/2520.

1/4*630/630=630/2520, 1/5*504/504=504/2520, 1/6*420/420=420/2520, 1/7*360/360=360/2520, 1/8*315/315=315/2520 and 1/9*280/280=280/2520.

Finally, add

(1260+840+630+504+420+360+315+280)/2520 which = 4609/2520.